基于信息理论框架的量子非马尔科夫特性的度量与应用研究

The difficulty inherent in the quantum theory leads to very few general results of quantum non-Markovianity, and the definition of a convenient notion of non-Markovian open quantum dynamics is still riddled with inconsistency and subtle variations. The research upon quantum non-Markovianity is one of the most popular subjects in the field of quantum information, and most of the previous studies are based on the master equations. The research of this quantum feature from the perspective of information theory has rapidly developed and many important theoretical and experimental progresses have been made. In this project, we will propose some new criteria to detect and quantify quantum non-Markovianity using quantum skew information and quantum correlations, and put forward the non-Markovian measures which involve less optimization procedure and are more convenient to implement in experiment. Then we will explore a unified framework to analyze the relationship between the previously proposed non-Markovian characterizations and study the properties such as additivity and transitivity. Furthermore, we will investigate the applications of quantum non-Markovianity in quantum estimation and decoherence suppression to see whether it can be used as a novel resource for quantum technology to improve the effectiveness of certain quantum tasks. The manipulation and utilization of this quantum feature using quantum control methods are also within the scope of this project.

由于量子理论的复杂性与结构的特殊性，量子非马尔科夫特性尚没有统一的刻画与度量标准。如何全面系统地认识和理解此量子特性是当前量子信息领域的一个热点问题。已有关于量子非马尔科夫特性的研究主要是从主方程的角度进行的。近年来，基于信息理论框架的量子非马尔科夫特性的分析，吸引了越来越多的科研人员的关注，并取得了一些重要的理论与实验进展。本项目将在信息理论的框架内，围绕量子非马尔科夫特性的度量及其在量子估计和退相干抑制中的具体应用展开研究。一方面，借助量子skew信息与量子关联等信息量，刻画量子非马尔科夫特性，提出便于实验实现与优化计算的度量准则，并分析其可加性、转移性等性质以及诸多度量之间的内在联系；另一方面，针对量子估计与退相干抑制问题，研究量子非马尔科夫特性的具体应用，并借助量子控制方法对这一潜在的量子信息处理资源加以调控与利用。

全面系统地认识和理解量子非马尔科夫特性是当前量子信息领域的一个热点问题。本项目旨在利用信息理论框架，研究量子非马尔科夫特性的度量及其在量子估计和退相干抑制问题中的具体应用。取得了如下研究进展：首先，从量子Rényi熵等角度提出了新型的量子非马尔科夫特新的判定与度量标准，并借助该度量统一了现有的基于冯诺依曼熵和Brukner-Zeilinger协变信息的非马尔科夫特性的判定准则，在不需要辅助量子系统的前提下，有效的刻画了信息在系统和环境之间的流动情况。其次，从量子系综的角度，研究了量子马尔科夫信道与完全退量子性信道之间的关系，为分析量子马尔可夫特性的本质属性和探讨记忆特性的来源问题，提供了理论支撑。再次，借助量子控制方法，完成了量子马尔科夫信道与非马尔科夫信道之间的转换，实现了对量子记忆特性的调控和利用。最后，利用信息理论方法，研究了量子相变问题，并指出其在提高量子测量精度和抑制量子退相干方面的潜在应用。所得结果有助于深化我们对量子非马尔科夫特性的认识和理解，为其在量子信息处理任务中的应用提供理论保障。